The only real Atheist is a dead Athiest. You have literally formed your whole premise off of the fact that there are no true atheists, as every atheist has a belief, which by definition, makes them a theist. This is too broadened of a definition of the word theist.
What you seem to overlook, is the fact that theists have fundamental beliefs about the singular governing entity of the universe. And that belief is predicated on no scientific evidence, and often times contradicts scientific evidence.
An atheist's fundamental belief system is based off of a malleable foundation, that is affected by scientific discovery, and is rooted in a logical, scientific paradigm. At this point it is not even a belief, but rather, the truth. You can choose to believe that 2+2 is 4, or you can choose not to, one is the wrong belief, and the other is simply true, regardless of belief or not. Similarly, an atheists belief if not as much of a belief, as it is true due to the aforementioned scientific foundation..
With regards to atheists's belief of the non existence of god, this, whilst can be viewed as a belief, is predicated on a scientific foundation, whilst a theists belief of the existence of god, is not.
To elaborate, one of the many discrepancies in the bible is, that the earth is 5000 years old. This is quite obviously contradictory to scientific discovery, and hence, modern science itself. Hence, the belief in the bible despite scientific evidence that suggests the contrary, is an illogical and unscientific belief. Therein lies the difference between an atheist and theist.
Idealistically (i say idealistically, to account for the people who are atheists but still believe in the tooth fairy, etc.) an atheist would never have a belief that is contradictory to scientific discovery and justification, whilst a theist does the opposite.